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In this study, the motion of a charged spin-1/2 fermion is found out. It is assumed, in the system, that the free fermion is subjected to a linearly space-dependent magnetic field that can be supposed to be a focusing magnetic field of a quadrupole magnet in beam dynamics in the accelerator physics. In such an examination, two-component Dirac equation is solved via perturbation approximation of the asymptotic iteration method (AIM), which has been widely used for the last decades. The results show that the fermion is bounded to the magnetic field for a certain condition of the strength of the field. For such a system, the analytical form of the energy eigenvalues are obtained. Moreover, to see whether this analytical expression works properly, the numerical eigenvalues are compared with the ones obtained by direct use of the AIM. We have an inspiration that the studies on beam dynamics and magnet design in particle accelerator physics may gain from this work. Key words: Dirac equation, asymptotic iteration method, perturbation theory, quadrupole magnet field, exact solutions, 1. Introduction According to our knowledge of basic quantum mechanics, if one wants to get information about a quantum mechanical system, it is needed to achieve the energy spectrum of [...]

In this study, we obtained exact solutions of the Feinberg-Horodecki equation for the time-dependent Wei-Hua potential, which is constructed by the temporal counterpart of the spatial form of this potential. We obtained the quantized momentum eigenvalues and the corresponding wave functions. We obtained the partition function for the system and studied other thermodynamic properties that include vibrational mean momentum (U), vibrational specific heat capacity (C), vibrational entropy (s), and vibrational free momentum (F) as a signature in the momentum space. Key words: bound states, Feinberg-Horodecki equation, time-dependent Wei-Hua oscillator, 1. Introduction It is well known that differential equations are the basis of many physical phenomena of nature. For example, quantum-mechanical phenomena are described by time-independent Schrodinger's equation, which dictates [...]

Clamping force is a crucial parameter in injection molding. Improper clamping force setting can result in poor product quality and shorter machine lifespan. The objective of this study was to establish an eigenvalue-injection clamping force peak value by real-time clamping force measurement with strain gage sensor for prediction, adjustment, and control of injection product quality. In this study, computer-aided engineering (CAE) structural analysis technique was used to analyze and verify the points of measurement of the sensor. Next, the molded product was conducted using the following injection molding parameters: V/P switchover point, clamping force, injection speed, melt temperature, mold temperature, packing pressure, and packing time. The relationship between injection clamping force peak value and product quality were examined. The results showed that CAE analysis could successfully predict and provide suitable points for sensor measurement. Comparison of analysis and experiment results revealed that injection clamping force peak value and part weight exhibited identical trends. Finally, the injection clamping force peak value not only could it successfully predict product qualify, but also it would achieve the purpose of optimizing and stabilizing the clamping force and part weight. KEYWORDS clamping force, injection clamping peak value, injection molding, intelligent, tie bar, 1 | INTRODUCTION Industry 4.0 is aimed at enabling machines to predict product qualify and correct parameters to achieve unmanned, automated production and increase machine availability and product yield rate, [...]

A new way of solving the spectral problem to describe electronic excitations is demonstrated for a hydrogen atom. The applied methodology is based formally on the idea of electronic excitation description without introducing boundary conditions to the eigenvalue problem for the square of the angular momentum operator. The eigenvalues of such an operator are considered as complex in general. As a result, the spectral problem for the Schrodinger equation becomes non-Hermitian with complex energy values. The imaginary part of the total energy helps to estimate the excitation lifetime within a unified scheme. The existence of the Stark shift of atomic energy levels and the collapse of the atomic spectra are confirmed. Key words: electronic structure, excited state properties, lifetime, total energy, hydrogen. Nous demontrons pour l'atome d'hydrogene une nouvelle facon de resoudre le probleme spectral dans la description des etats excites. La methodologie utilisee est basee sur l'idee de la description des excitations electroniques sans introduction de conditions limites au probleme de valeur propre pour le carre de l'operateur du carre du moment angulaire. Les valeurs propres de tels operateurs sont tenues comme complexes en general. Il en resulte que le probleme spectral pour l'equation de Schrodinger devient non-hermitien avec des energies complexes. La partie imaginaire de l'energie totale aide a estimer le temps de vie de l'excitation dans un schema unifie. Nous confirmons ainsi l'existence d'un decalage de Stark des niveaux d'energie et l'aplatissement des spectres atomiques. [Traduit par la Redaction] Mots-cles : structure electronique, proprietes des etats excites, temps de vie, energie totale, hydrogene., 1. Introduction The Schrodinger equation is a key subject in quantum mechanics [1]. It describes many problems in different branches of science. There are many ways to solve the Schrodinger [...]

Based on the Sturm-Liouville eigenvalue problem, we analytically study several properties of holographic s-wave superconductors with exponential nonlinear (EN) electrodynamics in the background of Schwarzschild anti-de Sitter black holes. We assume the probe limit in which the scalar and gauge fields do not back react on the background metric. We show that for this system, one can still obtain an analytical relation between the critical temperature and the charge density. Interestingly enough, we find that EN electrodynamics decreases the critical temperature, [T.sub.c], of the holographic superconductors compared to the linear Maxwell field. This implies that the nonlinear electrodynamics make the condensation harder. The analytical results obtained in this paper are in good agreement with the existing numerical results. We also compute the critical exponent near the critical temperature and find out that it is still 1/2, which seems to be a universal value in mean field theory. Key words: holographic superconductor, nonlinear electrodynamics, critical temperature. Sur la base du probleme aux valeurs propres de Sturm-Liouville, nous etudions analytiquement plusieurs proprietes de supraconducteurs holographiques d'onde s, avec l'electrodynamique non lineaire exponentielle (EN) sur un fond de trou noir de Schwarzschild anti-de Sitter. Nous supposons une limite dans laquelle les champs scalaire et de jauge n'ont pas de retroaction sur la metrique du fond. Nous montrons que dans ce systeme, on peut encore obtenir une relation analytique entre la temperature critique et la densite de charge. Assez interessant, nous trouvons que l'electrodynamique EN reduit la temperature critique, [T.sub.c] du supraconducteur holographique, compare au champ lineaire de Maxwell. Ceci implique que l'electrodynamique non lineaire rend la condensation plus difficile. Les resultats analytiques obtenus ici sont en bon accord avec les resultats numeriques existants. Nous calculons egalement l'exposant critique pres de la temperature critique et trouvons qu'il est encore 1/2, ce qui semble etre la valeur universelle en theorie de champ moyen. [Traduit par la Redaction] Mots-cles: supraconducteur holographique, electrodynamique non lineaire, temperature critique., 1. Introduction Nowadays, the correspondence between an anti-de Sitter (AdS) space-time and a conformal field theory (CFT) living on its boundary (AdS/CFT) is the well-known holographic picture of the world. [...]

A general class of potentials covering the Poschl-Teller-type and Scarf-type is considered. The analytical expression of the energy eigenvalues is established with the help of the exact quantization formula. Then, using appropriate coordinate transformations, the exact spectrums of five well-known potentials: Poschl-Teller, Poschl-Teller I and Poschl-Teller II, Scarf I, and Scarf II, are deduced in a simple way. Key words: analytical solution, exact quantization rule, Poschl-Teller-type, Scarf-type, energy levels. Nous etudions une classe generale de potentiels qui inclut les types de Poschl-Teller et de Scarf. La formule de quantification exacte nous permet d'obtenir des expressions analytiques pour les valeurs propres d'energie. Suite a un choix approprie de transformation de coordonnees, nous deduisons facilement les spectres exacts de cinq potentiels connus : Poschl-Teller, Poschl-Teller I, Poschl-Teller II, Scarf I et Scarf II. [Traduit par la Redaction] Mots-cles : solution analytique, regle de quantification exacte, type de Poschl-Teller, type de Scarf, niveaux d'energie. PACS Nos.: 03.65.Ca, 03.65.Ge., Introduction The field of research on analytical solutions of relativistic and nonrelativistic wave equations continues to arouse attention among scientists. In recent years, the problem of a particle submitted to [...]

The relativistic Duffin-Kemmer-Petiau equation for relativistic spin-1 particles with position-dependent mass in the presence of a vector Kratzer-type potential and the absence of a scalar potential is studied analytically. The energy eigenvalues and corresponding eigenfunctions are obtained using the wave function ansatz approach. PACS Nos.: 03.65.-w, 03.65.Ge, 03.65.Pm. Nous etudions ici analytiquement l'equation relativiste de Diffin-Kemmer-Petiau pour des particules de spin 1 avec une masse dependant de la position, en presence d'un potentiel vecteur du type Kratzer et en l'absence d'un potentiel scalaire. L'ansatz de la fonction d'onde nous permet d'obtenir les energies propres, avec les fonctions propres correspondantes. [Traduit par la Redaction], 1. Introduction Elementary particles hold integer and half-integer spins. While quarks and leptons are spin-1/2 fermions, and baryons are particles with spin-1/2 or -3/2, pseudoscalar mesons, such as the pion, [...]

Big ecological changes often involve regime shifts in which a critical threshold is crossed. Thresholds are often difficult to measure, and transgressions of thresholds come as surprises. If a critical threshold is approached gradually, however, there are early warnings of the impending regime shift. For example, in a one-dimensional ecosystem dynamics, autocorrelation approaches 1 from below, variance and skewness increase, and variance spectra shift to lower frequencies. Here we focus on variance, an indicator easily computed from monitoring data. There are two distinct sources of increased variance near a critical threshold. One is the amplification of small shocks that occurs as the square of the modulus of the leading eigenvalue (or leading pair of eigenvalues in the complex case) approaches 1 from below. This source, called 'squealing,' is well-studied. The second source of variance, called 'flickering,' involves brief excursions between attractors. Interacting regime shifts may muffle or magnify variance near critical thresholds. Whether muffling or magnification occurs, and the size of the effect, depend on the product of the feedback between the state variables times the correlation of these variables' responses to environmental shocks. If this product is positive, magnification of the variance will occur. If the product is negative, muffling or magnification can occur depending on the relative magnitudes of these and other effects. Therefore, monitoring programs should measure variates that have opposite responses to the critical transition. If the correlations to environmental shocks have the same sign, the variance of at least one variate will be magnified as the critical transition is approached. Simulation studies suggest that muffling may sometimes interfere with detection of early warning signals of regime shifts. However, more important effects of muffling and magnification may come from their effect on flickering, when random shocks trigger a state change in a system with low resilience. Muffling decreases the likelihood that a random shock will trigger a regime shift. Magnification has the opposite effect. Magnification is most likely when feedbacks are positive and state variables have positively correlated responses to environmental shocks. These results help delimit the conditions when regime shifts are more likely to cascade through complex systems. Key words: alternative stable states; critical thresholds; critical transition; early warning flickering; lakes; regime shift; squealing; trophic cascade; variance.